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Symmetric Hamilton Cycle Decompositions of Complete Multigraphs

100%

Chitra V., Muthusamy A.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 4

695-707

Let n ≥ 3 and ⋋ ≥ 1 be integers. Let ⋋Kn denote the complete multigraph with edge-multiplicity ⋋. In this paper, we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m for all even ⋋ ≥ 2 and m ≥ 2. Also we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m − F for all odd ⋋ ≥ 3 and m ≥ 2. In fact, our results together with the earlier results (by Walecki and Brualdi and Schroeder) completely settle the existence of symmetric Hamilton cycle decomposition of ⋋Kn (respectively, ⋋Kn − F, where F is a 1-factor of ⋋Kn) which exist if and only if ⋋(n − 1) is even (respectively, ⋋(n − 1) is odd), except the non-existence cases n ≡ 0 or 6 (mod 8) when ⋋ = 1

Decomposition of Complete Multigraphs Into Stars and Cycles

100%

Beggas F., Haddad M., Kheddouci H.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 4

629-639

Let k be a positive integer, Sk and Ck denote, respectively, a star and a cycle of k edges. λKn is the usual notation for the complete multigraph on n vertices and in which every edge is taken λ times. In this paper, we investigate necessary and sufficient conditions for the existence of the decomposition of λKn into edges disjoint of stars Sk’s and cycles Ck’s.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Beggas F.

1 Chitra V.

1 Haddad M.

1 Kheddouci H.

1 Muthusamy A.

1 2015

1 2013

Wyniki wyszukiwania

Symmetric Hamilton Cycle Decompositions of Complete Multigraphs

Decomposition of Complete Multigraphs Into Stars and Cycles